The disclosed subject matter relates to techniques for quantum key distribution, including high dimensional temporal quantum key distribution using dispersive optics.
Secure key distribution can be an important functionality for security in cryptographic systems. Generally, cryptographic systems are designed for secure transmission of private information between two parties (commonly referred to as Alice and Bob). Transmission of data over a classical communication channel involves the risk that an eavesdropper (commonly referred to as Eve) can intercept the data. To safeguard data transmitted over a classical communication channel, the data can be encrypted using a cryptographic key prior to transmission. However, in order to be decrypted, the cryptographic key must be known by the receiving party, and to further the objectives of the cryptographic system this key must not be known to any eavesdropper (i.e., the key is a shared secret between Alice and Bob). Accordingly, establishing a secret key (also referred to as a “private” key) between Alice and Bob is important to developing secure communication.
Quantum key distribution (QKD) is a technique that leverages the underlying physics of quantum mechanical interactions to ensure that shared keys are not intercepted by any third parties. Conventional QKD systems typically employ protocols utilizing photon polarization (or phase) states to encode data. For example, in the well known BB84 QKD protocol, a photon can be transmitted from Alice to Bob, each of which can prepare/measure the photons in non-orthogonal quantum “bases” (e.g., a rectilinear basis of polarization 0° and 90°; and a diagonal basis of polarization 45° and) 135°. Because these bases are non-orthogonal, no possible measurement distinguishes between the 4 different polarization states. That is, measurement in a rectilinear basis will result in a measurement of either 0° or 90°, even if the photons were prepared in a diagonal basis of 45° or 135°, introducing error for measurement in an incorrect basis.
Alice and Bob can randomly select which basis to prepare/measure in and share this information over a public channel. Measurements in the same basis can then be used to generate a secret key (e.g., measurements in the rectilinear basis of 0° can be assigned a binary value of 0, measurements in the rectilinear basis of 90° can be assigned a binary value of 1, measurements in the diagonal basis of 45° can be assigned a value of 0, and measurements in the diagonal basis of 135° can be assigned a value of 1). Because the basis of measurement is randomized, some of Eve's measurements will be made in a non-orthogonal basis, and such measurements will be incorrect 50% of the time. Additionally, measurements by Eve will introduce errors into the measurements of Bob and Alice. Accordingly, Alice and Bob can detect an eavesdropping event. Such a technique can generally be referred to as a “prepare and measure” QKD protocol (i.e., one party can prepare, and the other party can measure).
There exist certain techniques for QKD involving the use of measuring photons in unified bases. For example, the well known E91 and BBM92 protocols involve the use of entangled pairs of photons generated by a common source and transmitted to Alice and Bob. Alice and Bob can each measure in randomly selected bases as with the BB84 protocol. Such techniques can generally be referred to as an “entanglement based” QKD protocol (i.e., each party receives one photon from an entangled pair).
Protocols using polarization or phase states can be characterized by low dimensionality, resulting in low data rates. While degrees of freedom with higher dimensionality, such as position-momentum, energy-time, and orbital angular momentum can be utilized, they can be sensitive to external effects, reducing the practicality of such systems. Additionally, such systems can lack a “security proof” (i.e., the net information transmitted from Alice to Bob is positive after privacy amplification).